J maths 20

The goals scored by 40 football teams from three league divisions are recorded below

What is the total number of goals scored by all the teams?

If \(x\) is a positive real number, find the range of values for which \(\frac{1}{3x} + \frac{1}{2} > \frac{1}{4x}\).

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?

Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years.

In this figure, PQ = PR = PS and SRT = 68°. Find QPS

A sector of circle of radius 7.2cm which substends an angle of 300 degrees at the centre is used to form a cone. What s the radius of the base of the cone?

Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio

If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x.

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

Find the non-zero positive value of \(x\) which satisfies the equation
\[
\begin{vmatrix}
x & 1 & 0 \\
1 & x & 1 \\
0 & 1 & x
\end{vmatrix} = 0
\]

A cylindrical tank has a capacity of 3080m³. What is the depth of the tank if the diameter of its base is 14m?

In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offer both mathematics and physics?

In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12 degrees. How many students are offering physics?

Express the product of 0.0014 and 0.011 in standard form

What is the product of \(\frac{27}{5}, \; (3)^{-3} \; \text{and} \; \left(\frac{1}{5}\right)^{-1}\)

A binary operation x is defined by a x b = a^b. If a x 2 = 2 - a, find the possible values of a?

Reach each number to two significant figures and then evaluate (0.02174×1.2047)/ 0.023789

The pie chart shows the income of a civil servant in a month. If his monthly income is N6000, find his monthly basic salary.

Simplify \(\frac{324 - 4x^2}{2x + 18}\)

Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13

Find all real numbers \(x\) which satisfy the inequality \(\frac{1}{3}(x + 1) - 1 > \frac{1}{5}(x + 4)\)

Evaluate \((212)_3 - (121)_3 + (222)_3\)

Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

A crate of soft drinks contains 10 bottle of Coca-Cola 8 of Fanta and 6 of Sprite. If one bottle is selected at random, what is the probability that it is Not a Coca-Cola bottle?

In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represent meat in a pie chart?

Four boys and ten girls can cut a field first in 5 hours. If the boys work at 5/4 the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?

What is the circumference of latitude 0° S if R is the radius of the earth?

A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60 degrees. Calculate the height of the tank.

A surveyor walks 500m up a hill which slopes at an angle of 30 degrees. Calculate the vertical height through which he rises

Find the gradient of the line passing through the points (-2, 0) and (0, -4)

Find the equation of the line through the points (5, 7) parallel to the line 7x + 5y = 12.

The angle of a sector of a circle radius 10.5 cm is 48 degrees. Calculate the perimeter of the sector.

A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime

The equation of the line in the graph is

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

Factorize (4a + 3)² - (3a - 2)²

The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.

Find the value of \(x\) if \(\frac{\sqrt{2}}{x + \sqrt{2}} = \frac{1}{x - \sqrt{2}}\)

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.

If \(\log_{10} 2 = 0.3010\) and \(\log_{10} 3 = 0.4771\), evaluate \(\log_{10} 4.5\).